/ / ; a. . . (1) 



\ = fjr l -a. . (2) 



.so expressions for the focal distances of a point on the 

 In i>erbola are of the same form as those for the ellipse 

 Ml); here, however, e > 1 . 



: -, put ion (2) from equation (1) gives 



Vi-v,- 



hence, tk* difference between the focal tiiitancct of any point 



on an hyperbola i* constant; it it equal t th, fransverse axis. 



If the foci are not given, they may be constructed as 



follows, provided the semi-axes of the curve are known : plot 



nts ;!=(<i, 0) and = (0,6): th.-n with the center 



of the hyperbola as center, and the distance AB as radius, 



dejMTiln? a circle; it will cut the transverse axis in tht* 



required foci F l and F r for 



162. Construction of the hyperbola. Tht- |.r|M-rty of the 

 tnling article might be taken as a mew definition of the 



: the hyperbola it the locui of a point th< 

 >rhoe dittance* from two fjred points it constant. 

 a <lctinition leads at once to the equation <>f the curve 

 v. 6, p. 67), and also to a method for iu 





